Parameter Estimation for Stochastic Models of Fluvial Channel Reservoirs

Abstract

Stochastic modeling techniques are being used increasingly to describe the geometries of fluvial channel reservoirs as a basis for field development decisions such as optimal well configuration. One of the main problems associated with the application of such tools is the inference of the necessary input parameters to describe the models. It is difficult to estimate the lateral continuity and stacking pattern of the sandstone reservoirs. This paper will focus on the application of outcrop data sets for inferring realistic input parameters. Input to two different stochastic models is described: one simple model (a binary truncated Gaussian field), and one more complex model (a hierarchical marked-point model with spatial interaction functions). Parameters have been estimate from outcrops in Spain and the United States and the models have been tested on data from a North Sea oil field. Indicator variograms estimated from outcrops can be used to define the spatial correlation structure of a truncated Gaussian field and control the continuity of sandstones simulated using such a model. Although indicator variograms are only two-point statistics, they provide a reasonable description of sandstone geometries and correlation lengths reflect bed thicknesses and widths. The hierarchical marked-point model comprises a population of [open quotes]points[closemore » quotes] (lines in 3-D models), which describe the positions of channel belts. The spatial arrangement of the lines is partly controlled by interaction functions, which are used to define the (non-Poisson) distribution of the channel belts. Each channel belt is associated with a series of [open quotes]marks,[close quotes] which define the channel dimensions, number of channels, and channel stacking. Parameter estimation in this model is more complex, but typical values of parameters such as channel dimension, channel stacking patterns, and channel-belt stacking patterns have been estimated from outcrop data.« less